\newproblem{lay:6_1_16}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.1.16}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $\mathbf{u}=\begin{pmatrix}12\\3\\-5\end{pmatrix}$ and $\mathbf{v}=\begin{pmatrix}2\\-3\\3\end{pmatrix}$. Determine if both vectors are orthgonal.
}{
   % Solution
	$\mathbf{u}$ is orthogonal to $\mathbf{v}$ if their inner product is 0
	\begin{center}
		$\mathbf{u}\cdot \mathbf{v}=0$\\
		$12\cdot(2)+(3)\cdot(-3)+(-5)\cdot(3)=24-9-15=0$
	\end{center}
	So, they are orthogonal.
}
\useproblem{lay:6_1_16}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
